Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?trsna

Estimates condition numbers for specified eigenvalues and right eigenvectors of an upper (quasi-) triangular matrix.

Syntax

call strsna
(
job
,
howmny
,
select
,
n
,
t
,
ldt
,
vl
,
ldvl
,
vr
,
ldvr
,
s
,
sep
,
mm
,
m
,
work
,
ldwork
,
iwork
,
info
)
call dtrsna
(
job
,
howmny
,
select
,
n
,
t
,
ldt
,
vl
,
ldvl
,
vr
,
ldvr
,
s
,
sep
,
mm
,
m
,
work
,
ldwork
,
iwork
,
info
)
call ctrsna
(
job
,
howmny
,
select
,
n
,
t
,
ldt
,
vl
,
ldvl
,
vr
,
ldvr
,
s
,
sep
,
mm
,
m
,
work
,
ldwork
,
rwork
,
info
)
call ztrsna
(
job
,
howmny
,
select
,
n
,
t
,
ldt
,
vl
,
ldvl
,
vr
,
ldvr
,
s
,
sep
,
mm
,
m
,
work
,
ldwork
,
rwork
,
info
)
call trsna
(
t
[
,
s
]
[
,
sep
]
[
,
vl
]
[
,
vr
]
[
,
select
]
[
,
m
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine estimates condition numbers for specified eigenvalues and/or right eigenvectors of an upper triangular matrix
T
(or, for real flavors, upper quasi-triangular matrix
T
in canonical Schur form). These are the same as the condition numbers of the eigenvalues and right eigenvectors of an original matrix
A
=
Z*T*Z
H
(with unitary or, for real flavors, orthogonal
Z
), from which
T
may have been derived.
The routine computes the reciprocal of the condition number of an eigenvalue
λ
i
as
s
i
= |
v
T
*
u
|/(||
u
||
E
||
v
||
E
)
for real flavors and
s
i
= |
v
H
*
u
|/(||
u
||
E
||
v
||
E
)
for complex flavors,